Algebraic structures for pairwise comparison matrices: Consistency, social choices and Arrow’s theorem

Abstract: We present the algebraic structures behind the approaches used to work with pairwise comparison matrices and, in general, the representation of preferences. We obtain a general definition of consistency and a universal decomposition in the space of PCMs, which allow us to define a consistency index. Also Arrow’s theorem, which is presented in a general form, is relevant. All the presented results can be seen in the main formulations of PCMs, i.e., multiplicative, additive and fuzzy approach, by the fact that each of them is a particular interpretation of the more general algebraic structure needed to deal with these theories.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Algebraic structures for pairwise comparison matrices: Consistency, social choices and Arrow’s theorem ; volume:71 ; number:5 ; year:2021 ; pages:1047-1062 ; extent:16 ; Mathematica Slovaca ; 71, Heft 5 (2021), 1047-1062 (gesamt 16)

Contributors, Places and Time

• Creator: Barbieri, Giuseppina ; Boccuto, Antonio ; Vitale, Gaetano

Further information

• DOI: 10.1515/ms-2021-0038
• URN: urn:nbn:de:101:1-2022100114041671188303
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:37 AM CEST